Fibonacci numbers

» The true universal numbers

",, Chitwan Khosla
*~ Features Editor
M features
@theotherpress.ca

 

Ness are fascinating. Be it
the constants in numerous
laws of physics, the arrangement
of electrons in an atom, the value
of pi in math, or the Pythagorean
theorem, numbers have played a
key role in making complicated
phenomena easier to understand
and establish.

Technological advancement
and scientific developments owe
a lot to numbers, but numbers
are also critical in exploring the
marvels of nature. Have you ever
wondered why there are exactly
the same number of petals in a
lily flower and why they're in a
definite pattern? Have you ever
pondered why a species of fish
has the same pattern of fins? Or
why all humans have a specific
number of bones? All these

: questions are again answered

: by numbers. These numbers are
: called Fibonacci numbers. Often
: referred as nature’s numbering

: system, the Fibonacci numbers

: are a sequence of numbers

: which have a linear arithmetic

: progression pattern.

The basic series of Fibonacci

: numbers is 1, 1, 2, 3, 5, 8, 13, and

: so on. Some start the series from

: zero, but the pattern is definite:

: the next number is the sum of

: the previous two. Hence, the next
: number of the series should be 21 :
: (8 + 13). The set of numbers are
: fixed, and almost every known
: arrangement in nature follows

: this pattern.

Interestingly, we also observe

: a spiral pattern in nature which is
: formed by connecting the squares :
: with widths from Fibonacci

: numbers in an anti-clockwise

: fashion. This is called the golden
: spiral. If we divide anything

: the squares or rectangles of the

: width of Fibonacci numbers, we
: would have a pattern of golden

: rectangles. This is what we get

: to see in far-off galaxies and

: in hurricanes on the surface

: of Earth. We also witness the

: golden ratio which is a fixed

: number (1.618034 approx.). The
: ratio of any two consecutive

: Fibonacci numbers is equal

: to or approximately equal to

: the golden ratio. This ratio

: has supposedly been used in

: construction of the Pyramids of
: Giza as well as by Leonardo Da
Vinci.

Although various evidence

: shows that Fibonacci numbers

: were discovered and understood
: in ancient India, the modern

: world came to know about these
: in the 1200s from Leonardo

: Bonacci (Fibonacci), a famed

Italian mathematician. With

: his book, Liber Abaci, Bonacci

: introduced the world to the

: Hindu-Arabic numbering system
: and the Fibonacci numbers. He

: used the example of a pair of

: rabbits. Assuming that newly

: born male and female rabbits are

: rabbits would be there in the

: population at the end of the first

: year. On solving the puzzle, the

: solution was: one pair at the end

: of the first month, two pairs at

: the end of the second, three pairs
: at the end of the third, and then

: five pairs at the end of the fourth.
: The progression is now in the

: pattern of the Fibonacci numbers

: (1, 2,3, 5, &...).

The universe around is full

: of Fibonacci and golden ratio

: arrangements. The shell of a

: snail is in the pattern of a golden
: spiral. The centres of flowers

: show the spread of seeds in the

: progression of golden spirals.

: The arrangement of branching of :
: trees and stems, even the roots

: of the plants grow in the pattern
: of Fibonacci numbers. Apart

: from these examples, Fibonacci
: numbers are also a major part

: of music and other forms of art

: that we hear or see. Da Vinci's

Image from Thinkstock

: kept together and that the rabbits :
: are capable of breeding once they :
: are one month old, how many

Mona Lisa is a famous example.
It can be divided into the golden

: rectangles starting from the
: lady’s nose going in the clockwise
> manner.

The GoldenNumber.net

explains how music has roots

: in Fibonacci numbers. Many

: specialists and mathematicians

: believe that Mozart was aware

: of the importance of Fibonacci

: numbers in music. A single

: note has 13 notes in its span

: through its octave, and a scale

: is composed of eight notes. The

: fifth and the third notes are

: foundations of all the chords and
: are based a combinational tune of
: two steps and one step from the

: root tone which in turn is again

: the first note of the scale.

No matter if we believe in the

: logical reasoning of the Fibonacci
: numbers or we consider all this

: as a mere coincidence and an

: imaginative view of things, one

: thing is pretty evident: these

: numbers and patterns are truly

: magical!

 

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